Fighting behavior in male crickets is already well described, and some of the mechanisms underlying aggression and aggressive motivation have already been revealed. Much less is known about female/female interactions. Here, we report that adult female crickets that had been isolated for several days readily entered into agonistic interactions with conspecific individuals. Characteristic dyadic encounters between isolated females escalated in a stepwise manner and were concluded with the establishment of a dominant/subordinate relationship. For 15 to 30 minutes following an initial fight, former subordinate females showed a dramatic change in agonistic behavior. If they were paired with the former dominant opponent during this interval, a significant majority did not enter into any aggressive interaction but instead actively avoided the opponent. A similar experience-based and time-dependent increase in avoidance was observed when former subordinate females were paired with unfamiliar naïve opponents. However, when faced with an unfamiliar subordinate individual in the second encounter, no such increase in avoidance behavior was observed. We propose that the observed changes in the behavior of former subordinate females are the consequence of a change in the general state of arousal and of the recognition of dominance status, but not of individual recognition. The fact that former dominant individuals did not show similar experience-based changes in agonistic behavior suggests that dominant/subordinate relationships between pairs of female crickets are maintained mainly by the behavior of subordinate individuals.